A (2 - c(log n/n)) Approximation Algorithm for the Minimum Maximal Matching Problem

摘要

We consider the problem of finding a maximal matching of minimum size, given an unweighted general graph. This problem is a well studied and it is known to be NP-hard even for some restricted classes of graphs. Moreover, in case of general graphs, it is NP-hard to approximate the Minimum Maximal Matching (shortly MMM) within any constant factor smaller than 7/6. The current best known approximation algorithm is the straightforward algorithm which yields an approximation ratio of 2. We propose the first nontrivial algorithm yields an approximation ratio of 2-c(log n/n), for an arbitrarily positive constant c. Our algorithm is based on the local search technique and utilizes an approximate solution of the Minimum Weighted Maximal Matching problem in order to achieve the desirable approximation ratio.